Running Head: CORRELATION COEFFICIENT NONNORMALITY 1 Reducing Bias and Error in the Correlation Coefficient Due to Nonnormality
نویسندگان
چکیده
It is more common for educational and psychological data to be non-normal than to be approximately normal. This tendency may lead to bias and error in point estimates of the Pearson correlation coefficient. In a series of Monte Carlo simulations, the Pearson correlation was examined under conditions of normal and non-normal data, and it was compared to its major alternatives, including the Spearman rank-order correlation, the bootstrap estimate, the Box-Cox transformation family, and a generally normalizing transformation (i.e., rankit), as well as to various bias adjustments. Non-normality caused the correlation coefficient to be inflated by up to +.14, particularly when the non-normality involved heavy-tailed distributions. Traditional bias adjustments worsened this problem, further inflating the estimate. The Spearman and rankit correlations eliminated this inflation and provided conservative estimates. Rankit also minimized random error for most sample sizes, except for the smallest samples (n = 10), where bootstrapping was more effective. Overall, results justify the use of carefully chosen alternatives to the Pearson correlation when normality is violated.
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